| Title of paper:
|
On the extension of group-valued measures
|
| Author(s):
|
| Alžbeta Michalíková
|
| Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica
|
| alzbeta.michalikova@umb.sk
|
|
| Published in:
|
"Notes on Intuitionistic Fuzzy Sets", Volume 20, 2014, Number 4, pages 19–31
|
| Download:
|
 PDF (171 Kb, File info)
|
| Abstract:
|
Since any space of IF-sets can be embedded to an MV-algebra ([12]), and any MV- algebra can be presented as an interval in a lattice ordered group ([9]), it is interesting to study measures with respect to l-groups. In this paper the group-valued outer measures are studied. The main result is the Choquet lemma concerning lower continuity of the induced outer measure. The result is applied to the group-valued measure extension theorem.
|
| Keywords:
|
Measure, G-valued outer measure.
|
| AMS Classification:
|
03E72
|
| References:
|
- Atanassov, K., Intuitionistic Fuzzy Sets: Theory and Applications, Springer, Heidelberg, 1999.
- Atanassov, K., On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012.
- Carathéodory, C., Vorelsungen über reele Funktionen. Leipzig, Berlin 1927.
- Cignoli, R., I. M. L. D’Ottaviano, D. Mundici, Algebraic Foundations of Many-Valued Reasoning, Trends in Logic, Studia Logica Library, Vol. 7, Kluwer, Dordrecht, 2000.
- Fremlin, D. H., A direct proof of the Matthes–Wright integral extension theorem. J. London Math. Soc., Vol. 11, 1975, 276–284.
- Fremlin, D. H., Topological Riesz Spaces and Measure Theory, Cambridge Univ. Press, 1974.
- Michalíková, A., V. Valenčáková, Outer measure on F-sets, In: Proc. of 3rd International IEEE Conference Intelligent Systems, London, September 2006, 728–729.
- Michalíková, A., On the extension of Riesz space valued operators. Journal of Electrical Engineering, Vol. 57, 2006, No. 7/s, 89–91.
- Mundici, D., Interpretation of AFC*-algebras in Łukasiewicz sentential calculus, J. Funct. Anal., Vol. 65, 1986, 15–63.
- Riečan, B., Carathéodory measurability revisites. Tatra Moutnains Math. Publ., Vol. 34, 2006, No. 2, 321–332.
- Riečan, B., On measures and integrals with values in ordered groups. Math. Slovaca, Vol. 33, 1983, 153–163.
- Riečan, B., Analysis of Fuzzy Logic Models. In: Intelligent Systems (V. M. Koleshko ed.),INTECH 2012, 219–240.
- Riečan, B., T. Neubrunn, Integral, Measure, and Ordering. Kluwer Academic Publishers, Dordrecht and Ister Science, Bratislava, 1997.
- Wright. J. D. M., Stone-algebra-valued measures for vector lattices. Ann. Inst. Fourier (Grenoble), Vol. 21, 1971, 65–85.
|
| Citations:
|
The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.
|
|
